Improving the Pole Relocating Properties of Vector Fitting

TLDR

This paper proposes a modification to the vector fitting procedure for rational function approximation of frequency‑domain responses. The modification replaces the high‑frequency asymptotic requirement of the VF scaling function with a more relaxed condition. The modification yields significant performance gains, including improved pole relocation, faster convergence, better handling of noisy data, and enhanced wide‑band modeling of transmission lines, network equivalents, and transformers.

Abstract

This paper describes a modification of the vector fitting (VF) procedure for rational function approximation of frequency-domain responses. The modification greatly improves the ability of VF to relocate poles to better positions, thereby improving its convergence performance and reducing the importance of the initial pole set specification. This is achieved by replacing the high-frequency asymptotic requirement of the VF scaling function with a more relaxed condition. Calculated results demonstrate a major improvement of performance when fitting responses that are contaminated with noise. The procedure is also shown to be advantageous for wideband modeling of transmission lines, network equivalents, and transformers.